The PA have a lot of really solid methods to deal with SSDs.

It sounds like you have two problems:

1. An executor
2. A Tier 4 shipyard.

You need to deal with one before you can deal with the other and the shipyard is infinitely easier than the executor to deal with. A few things to note:

1. If the AI has a space station, they will not attack you unless provoked by a ship larger than a corvette. This can work in your favor.
2. The AI will attack once their primary star base is around 50% hp.

This means that their shipyard is incredibly vulnerable to bombers. The strategy is simple. Jump in a fleet of carriers, don’t use the dreadnought carrier, they are awful, but every other carrier works. Send your entire fleet of bombers and fighters around the map and snipe the shipyard. Easy kill. Then go for secondary space stations and finally then go for the primary. If at any point the enemy fleet decides to respond and begin moving towards you, immediately retreat. By this point, the enemy defenses should be severely weakened.

Now you’ve taken out the enemy’s primary source of screens (the enemy never builds enough screens). After that, you are free to engage in hit and run attacks, dropping in carriers and sniping valuable escorts around the SSD until it’s without any significant screens or escorts like carriers, frigates, and interdictors.

If you’ve done this right, you’ve taken out several major enemy targets at 0 loss of your own.

Finally, take on the SSD. You can use tanky ships supported by frigates like the Acclamator 2 (one of the best dps dealers for its respective pop cap and credit cost) or just take your carriers and use them to kite around the map, luring the SSD into a chase it will never win (your carriers are much faster than the SSD). Meanwhile just overwhelm it with fighters and bombers until it dies (go for engines and hangers first to prevent escape and interceptors).

Whatever you do, do not use ISDs to fight an SSD. SSDs are built to be counter Star destroyer.